Exact traversable wormhole solution in bumblebee gravity

Abstract

In this study, we found a new traversable wormhole solution in the framework of a bumblebee gravity model. With these types of models, the Lorentz symmetry violation arises from the dynamics of a bumblebee vector field that is non-minimally coupled with gravity. To this end, we checked the wormhole's flare-out and energy (null, weak, and strong) conditions. We then studied the deflection angle of light in the weak limit approximation using the Gibbons-Werner method. In particular, we show that the bumblebee gravity effect leads to a non-trivial global topology of the wormhole spacetime. By using the Gauss-Bonnet theorem (GBT), it is shown that the obtained non-asymptotically flat wormhole solution yields a topological term in the deflection angle of light. This term is proportional to the coupling constant, but independent from the impact factor parameter. Significantly, we showed that the bumblebee wormhole solutions, under specific conditions, support the normal matter wormhole geometries.